TESTING/EIG/sdrvbd.f(3)

NAME
TESTING/EIG/sdrvbd.f

SYNOPSIS

  Functions/Subroutines
subroutine sdrvbd (nsizes, mm, nn, ntypes, dotype, iseed, thresh, a, lda, u, ldu, vt, ldvt, asav, usav, vtsav, s, ssav, e, work, lwork, iwork, nout, info)
SDRVBD

Function/Subroutine Documentation

  subroutine sdrvbd (integer nsizes, integer, dimension( * ) mm, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, real, dimension( lda, * ) a, integer lda, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( lda, * ) asav, real, dimension( ldu, * ) usav, real, dimension( ldvt, * ) vtsav, real, dimension( * ) s, real, dimension( * ) ssav, real, dimension( * ) e, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer nout, integer info)

SDRVBD

Purpose:

    !>
    !> SDRVBD checks the singular value decomposition (SVD) drivers
    !> SGESVD, SGESDD, SGESVDQ, SGESVJ, SGEJSV, and DGESVDX.
    !>
    !> Both SGESVD and SGESDD factor A = U diag(S) VT, where U and VT are
    !> orthogonal and diag(S) is diagonal with the entries of the array S
    !> on its diagonal. The entries of S are the singular values,
    !> nonnegative and stored in decreasing order.  U and VT can be
    !> optionally not computed, overwritten on A, or computed partially.
    !>
    !> A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN.
    !> U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N.
    !>
    !> When SDRVBD is called, a number of matrix  (M's and N's)
    !> and a number of matrix  are specified.  For each size (M,N)
    !> and each type of matrix, and for the minimal workspace as well as
    !> workspace adequate to permit blocking, an  M x N  matrix  will be
    !> generated and used to test the SVD routines.  For each matrix, A will
    !> be factored as A = U diag(S) VT and the following 12 tests computed:
    !>
    !> Test for SGESVD:
    !>
    !> (1)    | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    !>
    !> (2)    | I - U'U | / ( M ulp )
    !>
    !> (3)    | I - VT VT' | / ( N ulp )
    !>
    !> (4)    S contains MNMIN nonnegative values in decreasing order.
    !>        (Return 0 if true, 1/ULP if false.)
    !>
    !> (5)    | U - Upartial | / ( M ulp ) where Upartial is a partially
    !>        computed U.
    !>
    !> (6)    | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
    !>        computed VT.
    !>
    !> (7)    | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
    !>        vector of singular values from the partial SVD
    !>
    !> Test for SGESDD:
    !>
    !> (8)    | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    !>
    !> (9)    | I - U'U | / ( M ulp )
    !>
    !> (10)   | I - VT VT' | / ( N ulp )
    !>
    !> (11)   S contains MNMIN nonnegative values in decreasing order.
    !>        (Return 0 if true, 1/ULP if false.)
    !>
    !> (12)   | U - Upartial | / ( M ulp ) where Upartial is a partially
    !>        computed U.
    !>
    !> (13)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
    !>        computed VT.
    !>
    !> (14)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
    !>        vector of singular values from the partial SVD
    !>
    !> Test for SGESVDQ:
    !>
    !> (36)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    !>
    !> (37)   | I - U'U | / ( M ulp )
    !>
    !> (38)   | I - VT VT' | / ( N ulp )
    !>
    !> (39)   S contains MNMIN nonnegative values in decreasing order.
    !>        (Return 0 if true, 1/ULP if false.)
    !>
    !> Test for SGESVJ:
    !>
    !> (15)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    !>
    !> (16)   | I - U'U | / ( M ulp )
    !>
    !> (17)   | I - VT VT' | / ( N ulp )
    !>
    !> (18)   S contains MNMIN nonnegative values in decreasing order.
    !>        (Return 0 if true, 1/ULP if false.)
    !>
    !> Test for SGEJSV:
    !>
    !> (19)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    !>
    !> (20)   | I - U'U | / ( M ulp )
    !>
    !> (21)   | I - VT VT' | / ( N ulp )
    !>
    !> (22)   S contains MNMIN nonnegative values in decreasing order.
    !>        (Return 0 if true, 1/ULP if false.)
    !>
    !> Test for SGESVDX( 'V', 'V', 'A' )/SGESVDX( 'N', 'N', 'A' )
    !>
    !> (23)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    !>
    !> (24)   | I - U'U | / ( M ulp )
    !>
    !> (25)   | I - VT VT' | / ( N ulp )
    !>
    !> (26)   S contains MNMIN nonnegative values in decreasing order.
    !>        (Return 0 if true, 1/ULP if false.)
    !>
    !> (27)   | U - Upartial | / ( M ulp ) where Upartial is a partially
    !>        computed U.
    !>
    !> (28)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
    !>        computed VT.
    !>
    !> (29)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
    !>        vector of singular values from the partial SVD
    !>
    !> Test for SGESVDX( 'V', 'V', 'I' )
    !>
    !> (30)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
    !>
    !> (31)   | I - U'U | / ( M ulp )
    !>
    !> (32)   | I - VT VT' | / ( N ulp )
    !>
    !> Test for SGESVDX( 'V', 'V', 'V' )
    !>
    !> (33)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
    !>
    !> (34)   | I - U'U | / ( M ulp )
    !>
    !> (35)   | I - VT VT' | / ( N ulp )
    !>
    !> The  are specified by the arrays MM(1:NSIZES) and
    !> NN(1:NSIZES); the value of each element pair (MM(j),NN(j))
    !> specifies one size.  The  are specified by a logical array
    !> DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type
    !> will be generated.
    !> Currently, the list of possible types is:
    !>
    !> (1)  The zero matrix.
    !> (2)  The identity matrix.
    !> (3)  A matrix of the form  U D V, where U and V are orthogonal and
    !>      D has evenly spaced entries 1, ..., ULP with random signs
    !>      on the diagonal.
    !> (4)  Same as (3), but multiplied by the underflow-threshold / ULP.
    !> (5)  Same as (3), but multiplied by the overflow-threshold * ULP.
    !>

Parameters
    NSIZES

    !>          NSIZES is INTEGER
    !>          The number of matrix sizes (M,N) contained in the vectors
    !>          MM and NN.
    !>

    MM

    !>          MM is INTEGER array, dimension (NSIZES)
    !>          The values of the matrix row dimension M.
    !>

    NN

    !>          NN is INTEGER array, dimension (NSIZES)
    !>          The values of the matrix column dimension N.
    !>

    NTYPES

    !>          NTYPES is INTEGER
    !>          The number of elements in DOTYPE.   If it is zero, SDRVBD
    !>          does nothing.  It must be at least zero.  If it is MAXTYP+1
    !>          and NSIZES is 1, then an additional type, MAXTYP+1 is
    !>          defined, which is to use whatever matrices are in A and B.
    !>          This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
    !>          DOTYPE(MAXTYP+1) is .TRUE. .
    !>

    DOTYPE

    !>          DOTYPE is LOGICAL array, dimension (NTYPES)
    !>          If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix
    !>          of type j will be generated.  If NTYPES is smaller than the
    !>          maximum number of types defined (PARAMETER MAXTYP), then
    !>          types NTYPES+1 through MAXTYP will not be generated.  If
    !>          NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through
    !>          DOTYPE(NTYPES) will be ignored.
    !>

    ISEED

    !>          ISEED is INTEGER array, dimension (4)
    !>          On entry, the seed of the random number generator.  The array
    !>          elements should be between 0 and 4095; if not they will be
    !>          reduced mod 4096.  Also, ISEED(4) must be odd.
    !>          On exit, ISEED is changed and can be used in the next call to
    !>          SDRVBD to continue the same random number sequence.
    !>

    THRESH

    !>          THRESH is REAL
    !>          The threshold value for the test ratios.  A result is
    !>          included in the output file if RESULT >= THRESH.  The test
    !>          ratios are scaled to be O(1), so THRESH should be a small
    !>          multiple of 1, e.g., 10 or 100.  To have every test ratio
    !>          printed, use THRESH = 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,NMAX)
    !>          where NMAX is the maximum value of N in NN.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,MMAX),
    !>          where MMAX is the maximum value of M in MM.
    !>

    U

    !>          U is REAL array, dimension (LDU,MMAX)
    !>

    LDU

    !>          LDU is INTEGER
    !>          The leading dimension of the array U.  LDU >= max(1,MMAX).
    !>

    VT

    !>          VT is REAL array, dimension (LDVT,NMAX)
    !>

    LDVT

    !>          LDVT is INTEGER
    !>          The leading dimension of the array VT.  LDVT >= max(1,NMAX).
    !>

    ASAV

    !>          ASAV is REAL array, dimension (LDA,NMAX)
    !>

    USAV

    !>          USAV is REAL array, dimension (LDU,MMAX)
    !>

    VTSAV

    !>          VTSAV is REAL array, dimension (LDVT,NMAX)
    !>

    S

    !>          S is REAL array, dimension
    !>                      (max(min(MM,NN)))
    !>

    SSAV

    !>          SSAV is REAL array, dimension
    !>                      (max(min(MM,NN)))
    !>

    E

    !>          E is REAL array, dimension
    !>                      (max(min(MM,NN)))
    !>

    WORK

    !>          WORK is REAL array, dimension (LWORK)
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The number of entries in WORK.  This must be at least
    !>          max(3*MN+MX,5*MN-4)+2*MN**2 for all pairs
    !>          pairs  (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) )
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension at least 8*min(M,N)
    !>

    NOUT

    !>          NOUT is INTEGER
    !>          The FORTRAN unit number for printing out error messages
    !>          (e.g., if a routine returns IINFO not equal to 0.)
    !>

    INFO

    !>          INFO is INTEGER
    !>          If 0, then everything ran OK.
    !>           -1: NSIZES < 0
    !>           -2: Some MM(j) < 0
    !>           -3: Some NN(j) < 0
    !>           -4: NTYPES < 0
    !>           -7: THRESH < 0
    !>          -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
    !>          -12: LDU < 1 or LDU < MMAX.
    !>          -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ).
    !>          -21: LWORK too small.
    !>          If  SLATMS, or SGESVD returns an error code, the
    !>              absolute value of it is returned.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 363 of file sdrvbd.f.

Author

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